# Thread: Describe A + B

1. ## Describe A + B

Hello. I don't know how to do this
A = { $(x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = { $(x_1,x_2): x_2=2, 0 \leq x_1 \leq 1$}

Describe A+B and A-B.

Thank you.

2. ## Re: Describe A + B

Well, these are line segments...

Do you know what "+" and "-" mean in this context?

3. ## Re: Describe A + B

Originally Posted by TheChaz
Well, these are line segments...
They look like coordinates to me.

Edit: I see what you mean. But + and - seem to me to be simple addition and subtraction of real coordinates.

4. ## Re: Describe A + B

Originally Posted by alexmahone
They look like coordinates to me.
Indeed, the elements of A and B are coordinates, but isn't the entire set A (B) a line segment/interval of R^2?

Since A and B aren't real numbers... ???

5. ## Re: Describe A + B

Originally Posted by Lolyta
Hello. I don't know how to do this
A = { $(x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = { $(x_1,x_2): x_2=2, 0 \leq x_1 \leq 1$}

Describe A+B and A-B.

Thank you.
A + B = { $(x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3$}
A - B = { $(x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1$}

6. ## Re: Describe A + B

Originally Posted by TheChaz
Indeed, the elements of A and B are coordinates, but isn't the entire set A (B) a line segment/interval of R^2?

Since A and B aren't real numbers... ???
Sorry...

7. ## Re: Describe A + B

Originally Posted by alexmahone
A + B = { $(x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3$}
A - B = { $(x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1$}
Thanks a lot for answering but could you explain how you did it?

8. ## Re: Describe A + B

Originally Posted by Lolyta
Thanks a lot for answering but could you explain how you did it?
We cannot help until you define what each of $A+B~\&~A-B$ means.

9. ## Re: Describe A + B

Originally Posted by Plato
We cannot help until you define what each of $A+B~\&~A-B$ means.
Well, A+B ={ $z: z = a+b : a\in{A}; b\in{B}$}.
A-B ={ $z: z = a-b : a\in{A}; b\in{B}$}.

10. ## Re: Describe A + B

Originally Posted by Lolyta
Hello. I don't know how to do this
A = { $(x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = { $(x_1,x_2): x_2=2, 0 \leq x_1 \leq 1$}
Describe A+B and A-B.
So it is coordinate operations.
Rewrite the B set to make the answer clearer.
A = { $(x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = $\{(x_1,x_2):0 \leq x_1 \leq 1, x_2=2\}$

Now
$A+B=\{x_1,x_2): 0\le x_1\le 1, 2 \leq x_2 \leq 1\}$

$A-B=\{x_1,x_2): -1\le x_1\le 0, -2 \leq x_2 \leq -1\}$

11. ## Re: Describe A + B

A + B = { $(x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3$}
A - B = { $(x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1$}